1909-10.] The Significance of the Correlation Coefficient, etc. 505 
Again the mating is unusual. The table of sires and dams for an 
offspring of colts is as follows : — 
Sires. 
Dams. 
Red. 
Roan. 
White. 
Red 
197 (217) 
277 (276) 
45 (27) 
Roan . 
221 (210) 
271 (268) 
12 (26) 
White . 
34 (26) 
28 (33) 
0(3) 
Alongside the actual figures are placed within brackets those required by 
random mating. It is seen at once that red matings with white or dominant 
with recessive are much more numerous than required by chance, a further 
cause of low correlation (par. 17). 
The values of the coefficient may now be considered. By the product 
method r = *363. By the fourfold table when normality is assumed 
r = ’46. If, however, the parentage is taken first, the expected Mendelian 
population of offspring calculated and the correlation evaluated, we find 
the aberrance of type among the offspring (the absence of sufficient whites) 
has lowered the correlation to some extent. A typical offspring for the 
parentage gives r = ’383. Professor Pearson by the contingency method 
gets r = ‘ 40, not greatly in excess of -363, and probably arrived at because 
he has made the calculation with the red group divided into three classes, 
and with this increase of division the contingency may be expected to give 
higher figures. In using the contingency method it is clearly not legitimate 
to break up one class without breaking up others, especially if one class, 
as seems here, is arbitrarily divided. 
One point remains to be considered : What is the correlation between 
parent and offspring among the different divisions of the dominants, as 
these, though of the same strain, have considerable variation of colour ? 
The table for sires and colts is as follows : — 
Sires. 
Colts. 
Red. 
Red with little White. 
Red and White. 
Red ... 
95 
/ 27 
13 
Red with little White . 
14 
6 
6 
Red and White . 
8 
4 
11 
